The warming rates of air temperature in high latitudes and high altitudes are greater than the rate of change in global average near-surface air temperature (e.g., Pepin et al., 2015). The greater climate warming has accelerated glacier melting and permafrost thawing in cold alpine regions, causing significant glacier and permafrost retreats (e.g., Yao et al., 2004, 2007) and landscape alternations (e.g., Niu et al., 2019). These changes undoubtedly alter the hydrodynamics of streamflow and groundwater storage in the alpine regions and their downstream tributaries (Bense et al., 2012; Walvoord and Striegl, 2007; Walvoord and Kurylyk, 2016; Li et al., 2018; Wang et al., 2018; Yi et al., 2021). A recent study of Wang et al. (2021) has shown that such changes have also caused changes in the precipitation–streamflow relationship. The societal impacts of these changes are profound because they redefine freshwater availability and its seasonality for populations of billions in the downstream tributaries (e.g., Cuo et al., 2014; Zhang et al., 2013; Wang et al., 2020).

Many studies have found that the compound effects of glacier and permafrost retreats in the past few decades have reshaped the groundwater flow and hydrological cycle (e.g., Bring et al., 2016; Forster et al., 2014; Ji et al., 2020; Walvoord and Kurylyk, 2016). The accelerated glacier melting and permafrost thawing have increased the soil active layer thickness (ALT) and therefore enlarged groundwater storage and allowed the exchange of surface water and groundwater (Xu et al., 2017; Forster et al., 2014; Ji et al., 2020). Such an exchange further alters streamflow composition in arctic catchments (Chang et al 2008; Walvoord and Kurylyk, 2016; Bring et al., 2016) and in the northeastern and southern Tibetan Plateau (TP; Li et al., 2018; Wang et al., 2018; Yi et al., 2021).

In those catchments, changes in groundwater storage and the subsurface moisture profile due to permafrost retreat could reroute subsurface flow paths during low flows (Koch et al., 2014; Payn et al., 2012). The thickened ALT allows infiltration through the previously permafrost layer into aquifers and thus increases the recharge in permafrost basins. It has been reported that the permafrost loss in the past decades has enhanced regional groundwater circulation (shortening its timescale) with more discharge to stream flows (Ji et al., 2020; Walvoord et al., 2012). As an example, the baseflow in the source region of the Yangtze River increased at a rate of 1.35 mma-1 during 1962–2012, following the annual temperature rise of 1.32 ∘C (Yi et al., 2021) and 1.09 mma-1 during 1979–2013 in glacierized basins in the TP, with its annual temperature rise of 0.98 ∘C (Lin et al., 2020). Walvoord and Striegl (2007) found that the groundwater contribution to streamflow in an arctic basin increased by 0.7 %–0.9 % per year from the 1950s to 2005, following its annual temperature rise of 1.24 ∘C during that period.

The effects of these changes in water budget and subsurface moisture profile on hydrographs are complicated in high altitude/frozen areas. The increase in ALT could reduce the buffering effect of soils on streamflow variability and thereby increase the baseflow recession rate (Lyon et al., 2009; Lyon and Destouni, 2010; Brutsaert and Hiyama, 2012). On the other hand, the increase in ALT enlarges groundwater storage and subsequently strengthens aquifer regulations on groundwater flow and slows the recession rate (Lin et al., 2020; Mao and Wang, 2016). These effects on the recession rate can result in the strongly nonlinear behavior of streamflow in time and space.

During periods of little or no precipitation, the baseflow recession (dQ/dt vs. Q, where Q is discharge) is typically described by a power law dQ/dt = - aQb (Brutsaert and Nieber, 1977; Tallaksen, 1995). The depletion of baseflow in relation to the parameters a and b contains valuable information concerning storage properties and aquifer characteristics of basins (Tallaksen, 1995). The recession-scale parameter a is a function of the hydraulic and geometric properties of the aquifer of a basin and can be used as a proxy for determining the effective depth of permafrost in frozen areas (Lyon and Destouni, 2010). The parameter b as reflected in the concavity of the hydrograph or the nonlinearity of recession (Dralle et al., 2017) is a function of boundary conditions to describe the equivalent water depth profile of an aquifer (Brutsaert and Nieber, 1977; Tashie et al., 2020). So, b can be interpreted as a measure of the diversity of water transport timescales throughout various parts of a catchment (Harman et al., 2009). Therefore, the variations in a and b in time and space can describe recession characteristics of a basin (e.g., Brutsaert and Nieber, 1977; Kirchner, 2009).

For the effects of a and b on the recession characteristics, Tashie et al. (2019) defined log(a) as the stability of streamflow and b as recession nonlinearity. For individual events, an increase in the relative value of a between events indicates decreased streamflow stability, while an increase in b indicates increased nonlinearity. Changes in the recession characteristics in time reflect their vulnerability to climatic and anthropogenic forcings (Berghuijs et al., 2016; Brooks et al., 2015; Buttle, 2018). Streamflow stability, log(a), has a significant seasonal cycle in over 99 % of the basins in the continental United States (Tashie et al., 2020). Moistening climate in catchments could increase the diversity of flow paths and the nonlinear relationships between storage/recharge and discharge (Brutsaert and Nieber, 1977; Hinzman et al., 2020). In cold climate regions, reduced glacier size can lead to considerable amplification of the seasonality of streamflow (Juen et al., 2007; Vuille et al., 2008). Hinzman et al. (2020) reported a widespread increase in the nonlinearity of recessions in northern Sweden due to climate warming. In addition, they found that this nonlinearity is significantly higher in warm winters than in cold winters. These analyses were performed under the assumption that a and b are effectively decorrelated. However, because changes in a in time are dependent on discharge Q, log(a) may be strongly correlated with b in individual events (Dralle et al. 2015; Biswal, 2021). Dralle et al. (2015) proposed a rescaling technique that eliminates the scale dependence of fitted power law parameters. Biswal (2021) selected the median of the values of b in individual events as the fixed b value and used it to find the event values of a.

In the southern TP, the Yarlung Zangbo River basin (YRB; Fig. 1a) has decades of observations and offers an opportunity to estimate variations in the recession characteristics of streamflow in glaciated areas of TP. Using those data, some recent studies have shown that the climate of the area has become warmer and wetter from 1980–2015 (e.g., Wang et al., 2021). Climate warming has reduced the buffering effect of glacial and permafrost on streamflow, leading to catchment property change with a shorter streamflow response time to precipitation (Wang et al., 2021). These changes must have affected streamflow recession characteristics.

The objective of this study is to investigate temporal and spatial variations in streamflow recession characteristics driven by climate and landscape changes in the glaciated basin of the YRB. The changes in these characteristics are examined using comparisons and contrasts of streamflow recessions indifferent subbasins and time periods according to the power law. To describe the temporal variability in the recession characteristics under climate warming, the decorrelation method by Dralle et al. (2015) is used to obtain a recession parameter a′ independent of b from individual recessions over the period of 1980–2015. Then, the a′ and b are regressed with mean temperature in recession periods for each subbasin of YRB. A sensitivity analysis reveals the effect of climate warming on the recession parameters, recession rates, and storage/recharge–discharge relations of different subbasins of YRB. They show the extent of the nonlinearity in the variation of the streamflow recessions in this glaciated basin of TP.

The YRB (28.2–31.2∘ N, 82.0–94.9∘ E) is the largest river basin in TP (Fig. 1). The main stem of YRB is formed by major suture zones in southern TP from the collision of the Indian plate and the Eurasian plate. The modern YRB flows along the suture from the west to the east before bending to the south at the eastern Himalayan syntaxes with an average west–east gradient of about 2.63 ‰ (Fig. 1a; Tan et al., 2021). In this study, we selected the upstream area of the great gorge of YRB (main stem about 1100 km, with an area of 2.0 × 105 km2). The elevation of the study area drops drastically from 6234 m in the west to 2030 m in the east (Yao et al., 2007; Wang et al., 2021).

Climate in YRB is heavily influenced by the Indian monsoon in summer and the westerlies in winter (Ren et al., 2018; Tian et al., 2020). From the west to the east of the basin, mean annual temperature varies from -9.3 to 22.0 ∘C, and the mean annual precipitation from 300 to 1050 mm. Nearly 90 % of the annual precipitation falls during June to September. As a result, the mean annual total streamflow of the entire basin, 289.7 mm is highly unevenly distributed in seasons. The summer streamflow is derived from monsoon rainfall and glacier meltwater. Groundwater accounts for about 55 % of the annual streamflow upstream and 27 % downstream of the YRB (Yao et al., 2021).

There are four hydrological stations along the main stem of YRB, namely LZ, NGS, YC, and NX, as shown in Fig. 1a. There are two additional hydrological stations, YBJ and LS, located in the major tributaries of the Lhasa River, which originates from the Nyainqêntanglha Mountains north of the YRB (Fig. 1a). Daily streamflow data from 1980 to 2015 are available at these hydrological stations, except for LZ. Accordingly, we divide YRB into five subbasins, with three nested subbasins of NGS, YC, and NX in the main stem of YRB and two subbasins of YBJ and LS in the tributaries of the Lhasa River.

There are four main dams/reservoirs (marked by the purple squares in Fig. 1a) in the YRB above the hydrological station of NX. The reservoirs, ML, ZK, PD, and ZM (Manla, Zhikong, Pangduo, and Zangmu, respectively), were built in 1999, 2003, 2007, and 2014, respectively. The reservoirs ML, PD, and ZM are operated daily, while ZK is operated seasonally. The impact of reservoir regulations on streamflow is minor for the subbasins NGS, YC, and NX in the main stem of the YRB because the reservoirs are operated daily and affect less than 10 % of the areas of the tributaries. In the tributary of the Lhasa River, the subbasin YBJ has no reservoirs while, the subbasin LS has two reservoirs, PD and ZK, which have impacts on streamflow.

Daily gridded data (0.1∘ × 0.1∘ spatial resolution) of precipitation (P) and mean surface air temperature (T) during 1980–2015 were provided by the National Tibetan Plateau Data Center (Yang and He, 2019; He et al., 2020; http://data.tpdc.ac.cn, last access: 26 November 2020). The subbasin-averaged P and T are calculated by the geometric mean of the gridded data.

Data of the glacier area and permafrost area, and the normalized difference vegetation index (NDVI) were collected from National Tibetan Plateau Data Center (Table 1; http://data.tpdc.ac.cn, last access: 26 November 2020). Glacier areas are located at altitudes from 3370 to 6460 m above sea level (Fig. 1a). Before 2000, the glacier and permafrost area accounted for 1.88 % and 41.8 % of the YRB area, respectively. These coverage percentages have reduced significantly since 2000 (Table 2). The annual mean NDVI was calculated using the maximum value synthesis method from the Global GIMMS NDVI3g v1 dataset, with a 15 d temporal resolution and 1/12∘ spatial resolution. The vegetation types are mainly alpine meadow, alpine steppe in the upstream (LZ), alpine shrubs and grasslands in the middle region (LZ-NGS), and alpine grassland and forest in the lower YRB (NGS-NX; Liu et al., 2014).

The annual depth of glacial melt data (G) during 1980–2015 is estimated using the degree day model (Su et al., 2015; Liu and Zhang, 2018). The calculation procedures are detailed in Wang et al. (2021). The annual ALT is estimated using a linear statistical function of the air freezing index (FIair) described in Xu et al. (2017), where FIair is calculated according to the cumulative value of daily mean temperature below 0 ∘C in a year.

After the warm season (June–September), there is little precipitation (Hayashi, 2020) in YRB, and the melting of the snow and glacier is minor due to cold temperatures (< -5 ∘C; Fig. 3). Subsequently, the flow discharge recedes from September to February of the following year. In this study, we use the daily discharge (Qt) in this recession period, which is defined as being from 1 October to 15 February of the following year, in our analysis of the recession process.

Observations have shown that climate warming has accelerated glacier melting and permafrost thawing in cold climate and high-altitude regions. Subsequent changes are found in vegetation growth and the thickening of talik and active soil layer thickness. These changes have altered land surface conditions and unconsolidated soil profiles and subsurface permafrost and thereby redefined the surface and groundwater exchange and balance in those regions (Fig. 10). Our case study of YRB in southern TP shows that accelerated glacier melting and permafrost thawing during 1980–2015 have substantially increased its dynamic groundwater storage, which is defined as S(Q)-S0=-∫Q0Qτ(Q)dQ. These results, with the decrease in terrestrial water storage (TWS) in the southern TP, including YRB (Wang et al., 2020) in recent decades, indicate a transformation of water storage in the region from a solid form (glacier and permafrost) to a liquid volume (soil moisture, surface water in rivers/lakes, and groundwater; Fig. 10b). According to the water balance in a catchment, i.e., dS/dt = Pr-E-Q, where S is regarded as the liquid volume (here, the change in S is equal to the sum of changes in soil moisture and groundwater), E is evapotranspiration, and Pr is the recharge from glacier melting, permafrost thawing, and precipitation, the increase in S infers that Pr is larger than the sum of E and Q in a study region. Because cold regions tend to have a greater coverage percentage of glacier and permafrost, glacier melting and permafrost thawing could substantially increase water storage under climate warming. Higher water storage could extend the recession period and sustain healthy annual streamflow.

Our study also shows that the increase in water storage and its effect on the annual recession of streamflow weakened towards the warmer downstream areas of YRB (with diminishing glacier melting and permafrost thawing effect). Accordingly, if the climate warming continues, the shrinking of the glacier and permafrost volume could eventually reach a point when there is not enough melting to recharge the liquid volume of water in YRB. From that point onward, steady streamflow in YRB would be in danger.

While the processes initiated by the accelerated glacier melting and permafrost thawing extend subsurface flow paths (Hinzman et al., 2020) and the streamflow recession time (τ), the increase in surface temperature and E can also increase surface water loss. According to the discharge relation -dQ/dt = -dQdSdSdt = (-Pr+E+Q)/τ (Kirchner, 2009), where Pr can be neglected in the recession period, a faster recession (-dQ/dt) could occur under climate warming from a faster decrease in storage (dS/dt) due to increasing E (Tashie et al., 2020), and a faster response of discharge to storage (dQ/dS) could occur due to the increase in the effective hydraulic properties (Lamontagne-Hallé et al., 2018). This phenomenon has happened for the initial recession period of 1–2 months when temperature is relatively higher (see Fig. 4).

Meanwhile, the accelerated glacier melting and permafrost thawing have shortened the frost period (i.e., the prolonged MTDa and MTDre in Fig. 2j and k) and thereby increased the soil active layer thickness (ALT) for groundwater storage (Lamontagne-Hallé et al., 2018) and lengthened subsurface flow paths (Hinzman et al., 2020) and the streamflow recession time (τ). These changes weaken the sensitivity of the discharge to the storage (dQ/dS = 1/τ) and slow down the recession rate (-dQ/dt), which is found in the later recession period when temperature is relatively lower (see Fig. 4). Therefore, the competing effects from the warming climate on dS/dt and dQ/dS in different recession phases would lead to the recession curve becoming more concave, which indicates an increase in the nonlinearity of the recession (b) and streamflow stability [log(a)] in YRB. In comparison, in the warm climate area, the effect of the storage decrease (dS/dt) on the recession (-dQ/dt) strengthens, and the effect of the recession timescale (1/τ or dQ/dS) on the recession weakens. As shown in Fig. 9, when temperature is higher (e.g., large and positive ΔT), hydrograph recession (negative ΔQ) is faster, along with the faster decline of storage (ΔS).

Additionally, deep circulating groundwater through macro structures, such as north–south-oriented active tensile faults (Fig. 1b), could also affect the baseflow and its recharge and discharge (Tan et al., 2021). According to studies using multi-tracer data (e.g., 2H, 3H, 18O, and Sr), modern meltwater is found to primarily maintain the rapid recharge of phreatic groundwater in alpine regions through faults and fissures (Shi et al., 2021). In the middle of the YRB (i.e., NGS–YC subbasins), changes in storage sensitivity to temperature (λTin Table 4) and recession timescale (τ) are greater than those in the upstream and downstream areas (NGS and NX subbasin, respectively). Rising temperature can greatly increase storage (Fig. 10b).

Finally, the anthropogenic effects from reservoir regulation can reduce the climate warming effect on these storage–discharge responses in the YRB. For example, in the LS subbasin, operations of two reservoirs significantly reduced the sensitivity of the recession parameters a (a′) and b to climate warming and increased streamflow stability [log(a)] (Fig. 4e). It remains questionable, however, as to how this human effort in water management in YRB would be practical/beneficial after the point when the increase in water storage from glacier and permafrost melt has exhausted the solid volume of water resources in the basin following climate warming.

Climate warming accelerated after 1997 in the Tibetan Plateau, especially in its cold and high-altitude upstream areas. Since 1997, the mean annual temperature has risen by 0.75–1.52 ∘C, and the mean temperature in the annual recession period (1 October–15 February of the following year) has risen by 1.40–1.78 ∘C in the five subbasins of the YRB. The largest rise in temperature occurred in the drier and colder subbasins in the upstream YRB. The recent strong warming has accelerated glacier melting and permafrost thawing, and thereby increased annual streamflow (12.7 %–31.5 % larger than the mean value in the early period before 1997) and streamflow in the recession period (20.9 %–25.8 % larger than before 1997) for the five subbasins, except LS where reservoir operations are active and heavily affecting the streamflow. These processes initiated by climate warming have changed the hydrological properties of subbasins considerably and altered the recession characteristics and the storage–discharge relationships.

We have found that the recession parameter a (a′) that characterizes the stability of streamflow has decreased exponentially in the subbasins, except for LS. Meanwhile, the parameter b that describes the nonlinearity of the recession to discharge has increased exponentially in all the subbasins. These results indicate that climate warming increases the nonlinearity of the recessions and enhances streamflow stability in most of the subbasins in YRB. Our sensitivity analysis further shows the decrease in the sensitivity of discharge/streamflow to storage under the warming climate. Currently, the accelerated glacier melting and permafrost thawing have recharged the system, deepening the active subsurface zone and increasing groundwater storage. Only a small fraction of the enlarged storage is released in surface streams because the increase in active water layer lengthens subsurface flow paths. These changes have also increased the recession timescale and retarded the recession in the later period, particularly in high-altitude cold climate areas. In the relatively warm climate areas downstream of the YRB, the effect of these changes is minor.

As the liquid water storage has increased greatly from melting glaciers and thawing permafrost in the YRB in the recent warming climate, the fast erosion of the solid water storage has weakened its buffering effect of the streamflow, which is becoming less stable and more vulnerable to individual intense precipitation events, such as increase in the recession rate in the initial period found in this study. There are the following two potential consequences from these changes: one is the increase in flash flooding in the trend of rising precipitation in the high-altitude subbasins where more land is exposed after the retreat of glaciers, and the other is the extreme scenario of exhaustion of the water resources in the upstream of the YRB after the buffering effect of glacier and permafrost is lost following the continued warming of the climate.

While human interference with these processes, via reservoirs and regulations, can reduce and curb these impacts of climate warming on storage–discharge relationships, recession characteristics, and streamflow in short term, as shown in the subbasin of LS, long-term strategies need to be developed to not only cope with the short-term needs but also the sustainability of water resources in the Tibetan Plateau under the threat of the continued warming that could change the entire hydrological system in this critical water source region for the one of world's most populated nations.